(4x-2)(4x-2)-36x^2=0

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Solution for (4x-2)(4x-2)-36x^2=0 equation: 


Simplifying
(4x + -2)(4x + -2) + -36x2 = 0

Reorder the terms:
(-2 + 4x)(4x + -2) + -36x2 = 0

Reorder the terms:
(-2 + 4x)(-2 + 4x) + -36x2 = 0

Multiply (-2 + 4x) * (-2 + 4x)
(-2(-2 + 4x) + 4x * (-2 + 4x)) + -36x2 = 0
((-2 * -2 + 4x * -2) + 4x * (-2 + 4x)) + -36x2 = 0
((4 + -8x) + 4x * (-2 + 4x)) + -36x2 = 0
(4 + -8x + (-2 * 4x + 4x * 4x)) + -36x2 = 0
(4 + -8x + (-8x + 16x2)) + -36x2 = 0

Combine like terms: -8x + -8x = -16x
(4 + -16x + 16x2) + -36x2 = 0

Combine like terms: 16x2 + -36x2 = -20x2
4 + -16x + -20x2 = 0

Solving
4 + -16x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -4x + -5x2) = 0

Factor a trinomial.
4((1 + -5x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {0.2, -1}

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